CBSE Class 12 Applied Mathematics Syllabus: 2020-21 (Revised & Reduced)

Download CBSE Class 12 Applied Mathematics Syllabus 2020-21 (Revised & Reduced) in PDF format. The link to download CBSE Syllabus for Class 12 Mathematics 2020-21 is given at the end of this article. Links to access other important articles are also available here.

Deleted CBSE Class 12 Syllabus 2020-21

CBSE Class 12 Applied Mathematics Syllabus: 2020-21 (Revised & Reduced)

One Paper, Three Hours - Max Marks: 80

Unit I Numbers, Quantification and Numerical Applications

⇒ Modulo Arithmetic

⇒Congruence modulo

⇒Simple arithmetic functions

⇒Allegation or Mixture

⇒Numerical problems on boats and streams; partnership; pipes and  cistern; races and games, scheduling

⇒Numerical inequalities

Unit II Algebra

⇒Solution of simultaneous linear equations using elimination method (up to 3 variables)

⇒Matrices and types of matrices

⇒Algebra of matrices

⇒Determinants

⇒Inverse of a matrix

⇒Cramer’s rule and  its application

⇒Simple applications of matrices and determinants including Leontiff input output model for two variables

Unit III Calculus

⇒Application of derivatives

⇒Increasing/Decreasing functions

⇒Maxima and Minima

⇒Marginal cost and marginal revenue using derivatives

⇒Integration

⇒Indefinite integral as family of curves

⇒Definite integral as area under  the curve

⇒Integration of simple algebraic functions (primitive, by substitution, by parts)

⇒Application of Integration (consumer surplus-producer surplus)

⇒Differential equation (definition, order,  degree)

⇒Formulating and solving linear differential equation

⇒Application of differential equation (Growth and  Decay  Model)

Unit IV Probability

⇒Probability Distribution

⇒Mathematical Expectation

⇒Variance

⇒Binomial Distribution

⇒Poisson distribution

⇒Normal distribution

⇒Basic applications and inferences

Unit V Inferential Statistics

⇒Population and sample

⇒Parameter, statistic and statistical inferences t-Test (one sample t-test and two independent groups t-test)

Unit VI Index numbers and Time-based data

⇒Index numbers, uses of index numbers

⇒Construction of index numbers (simple and  weighted)

⇒Tests of adequacy of index numbers (unit test and time reversal test)

⇒Time series, Time series analysis for univariant data  sets

⇒Trend  analysis by moving average method

⇒Trend  analysis by fitting of linear trend  line using least squares

Unit VII Financial Mathematics

⇒Perpetuity, Sinking funds

⇒Valuation of Bonds (Present value approach and  Relative price approach)

⇒Calculation of EMI

⇒Calculation of returns, nominal rate  of return,  effective rate of interest

⇒Compound annual growth rate

⇒Stock,  shares and debentures

⇒Linear method of depreciation

Unit VIII Linear Programming

⇒Introduction and related terminologies (constraints, objective function, optimization)

⇒Mathematical formulation of linear programming problems

⇒Different types of linear programming problems (Transportation and assignment problem)

⇒Graphical method of solution for problems in two variables

⇒Feasible and infeasible regions (bounded and unbounded)

⇒Feasible and infeasible solutions, optimal feasible solutions (up to three  non- trivial constraints)

Practical:  Use of spreadsheet

Graphs of exponential function, demand and supply functions on Excel and study the nature of function at various points, maxima/minima

Matrix operations using Excel

Suggested practical using the  spreadsheet

1.  Plot the graphs of functions on excel and study the graph  to find out point of maxima/minima;

2.  Probability and dice roll simulation;

3.  Matrix multiplication and inverse of a matrix;

4.  Stock Market data  sheet on excel;

5.  Collect the data  on weather, price, inflation, and pollution; analyze the data and  make  meaningful inferences;

6.  Collect data  from newspapers on traffic, sports activities and  on market  trends and  use excel to study future trends.

List of Suggested projects ( class XI /XII)

Use of prime numbers in coding and  decoding of messages; Prime numbers and divisibility rules;

Logarithms for financial calculations such as interest, present  value, future  vale, profit/loss etc., with large values);

Cardinality of a set and orders of infinity;

Comparing sets of Natural numbers, rational numbers, real numbers and others; Use of Venn Diagram in solving practical problems;

Fibonacci Sequence: Its’ history and presence in nature;

Testing the validity of mathematical statements and  framing truth tables; Investigating graphs of functions for their properties;

Visit the census site of India http://www.censusindia.gov.in/Census_Data_2001/Census_Data_Online/Language/ State ment3.htm Depict the information given there  in a pictorial form;

Prepare a questionnaire to collect information about  money  spent by your friends in a month  on  activities like traveling, movies, recharging of the  mobiles, etc.  and  draw interesting conclusions;

Check out the local newspaper and  cut  out  examples of information depicted by graphs. Draw your own conclusions from the graph  and  compare it with the analysis given in the report;

Analysis of population migration data – positive and negative influence on urbanization;

Each day the newspaper tells us about  the maximum temperature, minimum temperature, humidity. Collect the data  for a period of 30 days and represent it graphically. Compare it with the data  available for the same time period for the previous year;

Analysis career graph   of a  cricketer (batting average for a batsman and bowling average for a bowler). Conclude the  best year  of his career. It may  be  extended for other players also – tennis, badminton, athlete;

Vehicle registration data  – correlating with pollution and number of accidents;

Visit a village near  Delhi and collect data  of various crops over the past few years from the farmers. Also collect data  about  temperature variation and  rain over the period for a particular crop.  Try to find the  effect of temperature and  rain variations on  various crops;

Choose any week  of your ongoing semester. Collect data  for the past 10 – 15 years for the amount of rainfall received in Delhi during that week.  Predict amount of rainfall for the current  year;

Weather prediction (prediction of monsoon from past data);

Visit Kirana shops near  your home  and collect the data  of sale of certain commodities over a month.  Try to figure out the stock of a particular commodity which should be in the store in order  to maximize the profit;

Stock price movement ;

Risk assessments by insurance firms from data; Predicting stock market  crash;

Predicting outcome of election – exit polls; Predicting mortality of infants.

Assessment Plan  

1. Overall Assessment of the course is out of 100 marks.

2. Assessment plan consists of External Exam and  Internal Assessment.

3. External Exam  will be of 03 hours duration Paper/Pencil Test consisting of 80 marks.

4. Weightage of Internal Assessment is 20 marks. Internal Assessment can be  a  combination  of activities  spread throughout the semester/ academic  year. Internal Assessment activities include, projects and  excel based practical. Teachers can choose activities from the suggested list of practicals or they can plan activities of similar nature. For data  based practical, teachers are encouraged to  use data   from  local  sources to  make   it  more  relevant  for students.

5. Weightage for each area of internal assessment may be as under: